Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions
Gladys Narbona-Reina, Didier Bresch (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Springer Verlag (2010)] and in the present paper, we provide a self-contained description,...